simplifying this sqare root?

Question

simplifying square roots is easy, but i seem to have forgotten some rules.

When simplifying sqrt(80)

I get this:
sqrt(80)

sqrt(20*4)

4 sqrt(20)

4 sqrt (4*5) .... and i stop here. When taking the square root of the four to put on the outside, do i add it to the outside or multiply it?

oh ok thank you all very much. =]

Answer 1

multiply it, that's what you actually did in the previous steps
there was a "hidden '1'"

1 sqrt(80)

1 sqrt(20*4)

--you made a mistake here, you made the square root of 4 still 4--

2 sqrt(20)

2 sqrt (4*5)

4 sqrt (5)

^.^

Answer 2

Well you made a mistake when you simplified it the first time.

when you seperated the 80 into 20x4 you have to take the square root of 4 which is 2.

So it would look like 2 sqrt (4x5)

Than you take the square root of the 4 again, and times it by the two...making the final answer 4 sqrt (5)

A simple way to check if you did it correctly is to use a calculator and take the square root of the orginal equation, and than take the squaroot of the simplified equation multiplied by the outside numbers and see if they are the same.

I hope I helped.

Answer 3

You would multiply it.

But remember, you need to take the square root if you are moving a number out of the square root sign.
From sqrt (20*4) you should get 2*sqrt(20)
Then 2 sqrt(4*5) would be 4sqrt(5)

Answer 4

u went a little astray
root 80
=root20 X root 4
=root20 X 2 (which is the square root of 4)
=root4 X root 5 X 2
=2 X root5 X 2
=so the square root of 80 simplified is 4 root5


another way to do this is
root80=root16 X root 5
root16 = 4
root 80 = 4 X root 5

Answer 5

√80 = √(16 x 5) = 4√5

Answer 6

Well, you actually messed up in the beginning.

It's sqrt(80)
then 2 sqrt(20)
then 4 sqrt(5)

and you multiply.

Answer 7

sqrt(80)

sqrt (4 times 4 times 5)

sqrt (16 times 5)

the square root of 16 is 4

so we get: 4 sqrt of 5.

Answer 8

Just take 80 and divide by 2 to get 40, divide by 2 to get 20, divide by 2 to get 10, divide by 2 to get 5, divide by 5 to get 1. Since you divided by 2 four times and it is a square root, multiply two by two and get 4. Put the remaining 5 under a square root to get 4sqrt(5).

Answer 9

mutiply
sqrt(80) = 4*sqrt(5) (you had an error in your first step)
remeber sqrt(80) = sqrt(2^4*5) = 2^2*sqrt(5) = 4*sqrt(5)

here's another example
sqrt(288) = sqrt(2^5*3^2) = 2^2*3^1*sqrt(2^1) = 12*sqrt(2)

Answer 10

sqrt (80)
sqrt (4 *4*5)
4 sqrt(5)